Examples of special quadratic birational transformations into complete intersections of quadrics

Abstract

In our previous works (2012, 2013), we provided a finite list of properties characterizing all potential types of quadratic birational transformations of a projective space into a factorial variety, whose base locus is smooth and irreducible. However, some existence problems remained open. Among them one had to prove that the image of a given transformation was factorial, but in two particular situations, even the mere existence of the transformation was left as an open problem. In this paper, we use computer algebra methods to construct explicitly four examples of such transformations; two of them were among those for which it was not known that the image was factorial, and the other two show the existence of the two above referred transformations.

Accepted for publication in the Journal of Symbolic Computation

References in corpus (7)

• Varieties with quadratic entry locus, I
• On special quadratic birational transformations of a projective space into a hypersurface
• Quadro-quadric special birational transformations of projective spaces
• On special quadratic birational transformations whose base locus has dimension at most three
• Special birational transformations of projective spaces
• On special quadratic birational transformations of a projective space
• Quadro-quadric special birational transformations from projective spaces to smooth complete intersections

Cited by in corpus (3)

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